A trust-region method for nonlinear bilevel programming: algorithm and computational experience

We consider the approximation of nonlinear bilevel mathematical programs by solvable programs of the same type, {\it i.e.}, bilevel programs involving linear approximations of the upper-level objective and all constraint-defining functions, as well as a quadratic approximation of the lower-level objective. We describe the main features of the algorithm and the resulting software. Numerical experiments tend to confirm the promising behavior of the method.